Express your answer as a mixed number simplified to lowest terms. $6\dfrac{2}{6}-2\dfrac{2}{3} = {?}$
Solution: Simplify each fraction. $= {6\dfrac{1}{3}} - {2\dfrac{2}{3}}$ Find a common denominator for the fractions: $= {6\dfrac{1}{3}}-{2\dfrac{2}{3}}$ Convert ${6\dfrac{1}{3}}$ to ${5 + \dfrac{3}{3} + \dfrac{1}{3}}$ So the problem becomes: ${5\dfrac{4}{3}}-{2\dfrac{2}{3}}$ Separate the whole numbers from the fractional parts: $= {5} + {\dfrac{4}{3}} - {2} - {\dfrac{2}{3}}$ Bring the whole numbers together and the fractions together: $= {5} - {2} + {\dfrac{4}{3}} - {\dfrac{2}{3}}$ Subtract the whole numbers: $=3 + {\dfrac{4}{3}} - {\dfrac{2}{3}}$ Subtract the fractions: $= 3+\dfrac{2}{3}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{2}{3}$